Rewrite as a simplified fraction. ${0.\overline{65} = {?}}$
Explanation: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 65.6565...\\ 1x &= 0.6565...\end{align*}}$ Subtracting the two equations, we have: ${99x = 65}$ ${x = \dfrac{65}{99}} $